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Preventive maintenance for homogeneous and heterogeneous systems

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  • Maxim Finkelstein
  • Gregory Levitin

Abstract

We consider optimal preventive maintenance for homogeneous and heterogeneous systems with major (critical) and minor (noncritical) failures. A major failure results in a replacement of a failed system, whereas minor failures can be minimally instantaneously repaired. Distinct from the homogeneous case, where the process of minimal repairs is the Poisson process, the process of minimal repairs in the heterogeneous case is the mixed Poisson process that does not possess the memoryless property. This enables considering the number of minimal repairs as the decision parameter for the corresponding optimal preventive maintenance policy. The proposed approach is theoretically justified, and the detailed illustrative numerical examples are presented.

Suggested Citation

  • Maxim Finkelstein & Gregory Levitin, 2019. "Preventive maintenance for homogeneous and heterogeneous systems," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 35(3), pages 908-920, May.
    • Handle: RePEc:wly:apsmbi:v:35:y:2019:i:3:p:908-920
    DOI: 10.1002/asmb.2422
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    1. Maxim Finkelstein, 2008. "Failure Rate Modelling for Reliability and Risk," Springer Series in Reliability Engineering, Springer, number 978-1-84800-986-8, March.
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    Cited by:

    1. Vladimir Rykov & Olga Kochueva & Yaroslav Rykov, 2021. "Preventive Maintenance of the k -out-of- n System with Respect to Cost-Type Criterion," Mathematics, MDPI, vol. 9(21), pages 1-15, November.
    2. Vladimir Rykov & Olga Kochueva, 2023. "Preventive Maintenance of k -out-of- n System with Dependent Failures," Mathematics, MDPI, vol. 11(2), pages 1-17, January.
    3. Vladimir Rykov & Olga Kochueva & Elvira Zaripova, 2023. "Renewable k -Out-of- n System with the Component-Wise Strategy of Preventive System Maintenance," Mathematics, MDPI, vol. 11(9), pages 1-21, May.

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